A correspondence between Intuitionistic logic and typed λ-calculus is well-known as Curry-Howard isomorphism. M.Parigot (1992) has extended the correspondence and introduced λμ-calculus as a second-order classical logic. λμ-calculus is a natural extension of λ-calculus and the system itself is quite interesting as a functional computation model. In the last two years' project, we have investigated the following points :(1)CPS-translation from type-free and simply typed λμ-calculi intoλ-calculus ;(2)Continuation denotational semantics of λμ-calculus and C-monoid ;(3)Similarity relation on CPO between CPS-translation and continuation denotational semantics.In order to extend the results above, we introduced a new system, an existential type system λ∃. It is proved that there exist bijective translations between polymorphicλ-calculus and a subsystem of λ∃, which form a Galois connection and moreover Galois embedding. From a programming point of view, this result means that polymorphic functions can be represented by abstract data types.